Method for determining an inflow profile in a multilayer well

ABSTRACT

A bottomhole temperature and a bottomhole pressure in a well are measured by means of sensors mounted on a perforation string below all perforation intervals. The measurements are made prior to perforating the well and after perforating the well until a temperature of a produced fluid returns to an initial reservoir temperature. Then the temperature of the produced fluid is measured by means of temperature sensors mounted on the perforation string above each perforation interval and a total production rate of the well is estimated. An excessive thermal energy of the produced fluid is calculated for each temperature sensor mounted on the perforation string above the perforation intervals and production rates of the individual perforation intervals are determined based on the calculated excessive thermal energies of the produced fluid and the known number of perforating charges in each perforation interval.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to Russian Application No. 2016150448 filed Dec. 21, 2016, which is incorporated herein by reference in its entirety.

BACKGROUND

The disclosure relates to the field of geophysical exploration of oil and gas wells, namely to determination of an inflow profile of a produced fluid in multilayer wells with several perforation intervals.

Determination of an inflow profile from a multilayer well is an important problem. Determination of a production rate of individual perforation intervals is necessary, in particular, for making a decision on the need for acid treatment, repeated perforation, etc.

Determination of an inflow profile is performed usually during production logging of an exploitation well using mechanical flow meters (see, for example, Hill, A.D., Production Logging—Theoretical and Interpretive Elements, SPE Monograph Series., 2002, p. 61). The main drawbacks of this method are the need to conduct a special well logging (in addition to the operations carried out in the well during perforation and well testing) and difficulty in determining production rates of low-yield formations.

The contribution of different perforation intervals can also be estimated using the temperature logging data of the exploitation well (see Cheremensky G. A., Applied Geothermy, M. Nedra, page 181) or basing on the analysis of non-stationary temperature data obtained by changing flow rate of a well (see Chekalyuk, E. B., Thermodynamics of the oil reservoir, Moscow, 1965, page 88, or Ramazanov, A., Valiullin, R. A., Shako, V., Pimenov, V., Sadretdinov, A., Fedorov, V., Belov, K., 2010. Thermal Modeling for Characterization of Near Wellbore Zone and Zonal Allocation, SPE 136256-MS). The drawbacks of these methods include the need to analyze relatively small temperature signals and the need to conduct special loggings of the well or to mount the special equipment in the well.

SUMMARY

In accordance with the proposed method, a bottomhole temperature and a bottomhole pressure measurements are made by means of sensors mounted on a perforation string below all perforation intervals and by means of temperature sensors mounted on the perforation string above each perforation interval.

The temperature and bottomhole pressure measurements are made prior to perforating the well and after perforating until a temperature of the produced fluid returns to an initial reservoir temperature. A total production rate of the well is estimated and an excessive thermal energy of the produced fluid is calculated for all temperature sensors mounted on the perforation string above the perforation intervals, and then the production rate of the individual perforation intervals is determined based on the calculated excessive thermal energy of the produced fluid and the known number of perforating charges in each perforation interval.

In accordance with one embodiment of the disclosure, the total production rate of the well is determined by measuring a flow rate at the surface or in the well.

According to another embodiment of the disclosure, the total production rate of the well is determined by calculating a flow rate based on the change in the bottomhole pressure.

In accordance with another embodiment of the disclosure, the total production rate of the well is determined by calculating a flow rate using the bottomhole pressure and numerically simulating the multilayer exploitation well.

BRIEF DESCRIPTION OF DRAWINGS

The disclosure is illustrated by the drawings, where FIG. 1 shows a schematic diagram of a well with two perforation intervals, FIG. 2 shows an example of the bottomhole pressure P₀(t) and temperatures of the produced fluid T₁(t) and T₂(t) above the perforation intervals, FIG. 3 shows a production rate of the well calculated for the pressure shown in FIG. 2, FIG. 4 shows total excessive thermal energy of the produced fluid (calculated from temperature T₂, solid line) and the corresponding energy calculated from the temperature T₁, FIG. 5 shows the algorithm for determining the inflow profile using numerical simulation of the multilayer exploitation well.

DETAILED DESCRIPTION

The disclosure proposes to determine the inflow profile in wells having several perforation intervals using well pressure measurement results and temperature measurement results by means of sensors mounted on a perforation column. The temperature should be measured above each perforation interval and at the bottom of the well, below all perforation intervals.

The method comprises measuring a bottomhole pressure P₀(t) and a bottomhole temperature T₀(t), which determines an average rock temperature in a depth interval under consideration. The measurements are made by means of sensors mounted on the perforation string in the well below all perforation intervals and also by measuring the temperature T_(i)(t) of the produced fluid (i=1, 2, . . . , m, m is a number of the perforation intervals) by means of temperature sensors mounted on the perforation string above each perforation interval.

The measurements of the pressure P₀(t) and temperature T_(i)(t) (i=0, 1, . . . , m) start before perforation (which allows to determine formation pressure and geothermal temperature) and the measurements continue for several hours after the perforation, until the temperature of the produced fluid, heated by the energy of the perforation explosion, returns to an initial reservoir temperature. When perforating charges are exploded, part of the energy is spent on evaporation of the well fluid and on the energy of the cumulative jet, but most of the energy is spent on heating the perforation string, a casing pipe and the rock near the well. Heating of the produced fluid occurs when it comes into contact with these bodies.

The total production rate of the well Q(t) is then evaluated using one of the following methods:

-   -   measurement of a flow rate at the surface or in the well,     -   calculation of the flow rate by changing the bottomhole pressure         P₀(t) (if the produced fluid does not reach the surface),     -   calculation of the flow rate using the bottomhole pressure P₀(t)         and numerical simulation of the multiplayer exploitation well.

The parameters (permeability and skin factors) that determine the productivity of individual formations are assumed to be equal to the mean values, which are determined by the traditional hydrodynamic exploration of the well.

The excessive thermal energy of the produced fluid for each temperature sensor is calculated

E _(i)=ρ_(fl) c _(fl) ·∫Q(t)[T _(i)(t)−T _(f)](i=1, . . . ,m),

where T_(f) is an average rock temperature in the considered depth interval (determined by T₀(t) and practically equal to it), ρ_(fl)c_(fl) is a volumetric heat capacity of the fluid.

Production rate of individual perforation intervals is calculated from the values E_(i) and the known amounts of perforating charges in each perforation interval.

Let us consider the case of a low-rate well, when during the first hours after the perforation there is no flow of the produced fluid onto the surface.

A schematic diagram of the well with a perforation string, a packer and two perforation intervals is shown in FIG. 1, which depicts a packer—1, a valve—2, a temperature sensor T₂—3, a temperature sensor T₁—4, a bottom-hole temperature sensor and a pressure sensors T₀, P₀—5, a second inflow zone—6, a first inflow zone—7, a second perforation interval—8, a first perforation interval—9.

FIG. 2 shows a synthetic example of the bottomhole pressure P₀(t) and temperatures of the produced fluid T₁(t) and T₂(t) above the perforation intervals. The thick curve corresponds to the bottomhole pressure, which is ˜50 bar before perforation and increases to the pressure of the formation (about 85 bar) during production in accordance with the fact that the fluid level rises in the production pipe. In this case, it is assumed that the perforation intervals have the same length and the same number of perforating charges.

If there is no flow of the produced fluid onto the surface, the total production rate of the well Q(t) can be calculated from the bottomhole pressure P₀(t):

${Q(t)} = {\frac{\pi \cdot r_{ti}^{2}}{\rho_{fl} \cdot g} \cdot \frac{{dP}_{0}}{dt}}$

where r_(t) is the internal radius of the pipe, g=9.81 m/s² is gravity acceleration, ρ_(fl)—density of fluid.

FIG. 3 shows the production rate of the well calculated by this formula for the pressure shown in FIG. 2 (for ρ_(fl)=850 kg/m³, r_(t)=0.038 m). The calculated production rate is then used to determine the inflow profile.

In the event that the total production rate of the well was measured in the well or at the surface, this production rate is directly used for determining the inflow profile.

The charts of temperature T₁ and T₂ (FIG. 2) show that immediately after the perforation, the flow temperature of the produced fluid is much greater (in this case by ˜20 C) than the temperature of the rocks T_(f) (points in FIG. 2). This temperature is determined by heating the well fluid during explosion and by heating the formation fluid when it comes into contact with the hot rock, the casing string and the perforation string. It should be noted that the temperature of the rock can be estimated from the results of measuring the temperature in the well before perforation.

The flow of reservoir fluid cools the near-wellbore rock, casing string and perforation string and in several hours (t_(p)=5÷10 hours) after the perforation, the temperatures measured in the well approach the unperturbed rock temperature (FIG. 2). This means that the thermal part E_(m), of the explosion energy of the perforating charges was transformed into the excessive thermal energy of the produced fluid.

In this case m=2 and E_(m)≡E₂. Using the temperature T₂, measured by the sensor, which is located above all perforating intervals, and the production rate of the well Q(t), this energy can be calculated by the formula:

E₂(t) = ρ_(fl)c_(fl) ⋅ ∫₀^(t)Q(t) ⋅ [T₂(t) − T_(f)]dt

The solid line in FIG. 4 shows the excessive thermal energy of the produced fluid for the data shown in FIG. 2. It is seen that in ˜3 hours after the perforation E₂ reaches its highest value E₂≈16.5 MJ.

The total energy of the perforation explosion, calculated based on the specific energy of the explosion and the mass of the explosive, in this case is E_(e)≈28 MJ. This means that approximately δ=60% of the explosion energy was converted into the thermal energy of the rock, the casing string and the perforation string:

E _(m) =δ·E _(e)

The remaining part of the explosion energy (about 40%) was spent on rock destruction, generation of shock waves in the rock and in the well, or it was quickly moved beyond the considered interval with the gaseous products of the explosion.

The procedure for calculating the production rate of the individual perforation intervals, proposed in the present disclosure, is based on the following assumptions:

-   -   the value δ is the same for different perforation intervals,     -   fluids entering the well from different perforation intervals         have the same volumetric heat capacities,     -   a distance between the perforation intervals is small and the         loss of fluid thermal energy to the surrounding rocks between         the perforation intervals can be neglected,     -   production duration after perforation and the production rate of         the well are large enough so that the fluid temperature measured         by the sensors is reduced to the temperature of the unperturbed         rocks.

Let m is a number of perforation intervals,

Q_(i) is a production rate from an i^(th) interval,

$Q = {\sum\limits_{j = 1}^{m}\; Q_{j}}$

is a total production rate of the well,

$\gamma_{i} = {\frac{1}{Q} \cdot {\sum\limits_{j = 1}^{i}\; Q_{j}}}$

is a production rate of the well from the lower i perforation intervals, referred to the total production rate of the well (γ_(m)=1), n_(i) is a number of perforating charges in the i^(th) perforation interval,

$N = {\sum\limits_{j = 1}^{m}\; n_{j}}$

is a total number of perforating charges in the well,

$b_{i} = {\frac{1}{N} \cdot {\sum\limits_{j = 1}^{i}\; n_{j}}}$

a number of charges in the lower i perforation intervals, referred to the total number of perforating charges in the well (b_(m)=1), T_(i)(t) is the fluid temperature measured by the temperature sensor located above the i^(th) perforation interval.

The production rate of the individual perforation intervals (at the initial stage of the value γ_(i)) is calculated using the energy conservation law, which is recorded for all intervals (i=1, 2, . . . m):

b_(i) ⋅ ρ_(fl)c_(fl) ⋅ ∫₀^(t)Q(t) ⋅ [T_(m)(t) − T_(f)] dt = ρ_(fl)c_(fl) ⋅ ∫₀^(t)Q(t) ⋅ γ_(i) ⋅ [T_(i)(t) − T_(f)] dt   or $\mspace{20mu} {\gamma_{i} = {b_{i} \cdot \frac{E_{m}(t)}{E_{i}(t)}}}$

where i=1, 2, . . . m,

E_(i)(t) = ρ_(fl)c_(fl) ⋅ ∫₀^(t)Q(t) ⋅ [T_(i)(t) − T_(f)]dt

The required relative productivity

$y_{i}\left( {{y_{i} = {O_{i}/Q}},{{\sum\limits_{i = 1}^{m}\; y_{1}} = 1}} \right)$

of the individual perforation intervals is calculated by the formulas:

y ₁=γ₁

y ₂=γ₂−γ₁

y ₃=γ₃−γ₂

In the case of two perforation intervals (m=2) and the same number of perforating charges in the intervals (b₁=0.5) the calculated energy E₁(t) is shown in FIG. 4 by the dotted line.

The calculated value of the dimensionless production rate γ₁(t) is approximately constant value after ˜3 hours after perforation: γ₁=y₁≈0.7.

In general, non-stationary well production rate Q(t) can be calculated using the measured bottomhole pressure P₀(t) and the numerical model of a multilayer exploitation well, which includes the permittivity {k_(i)} and skins {s_(i)} of the productive formations as free parameters. The values of these parameters can be found using an iterative procedure, the algorithm of which is shown in FIG. 5.

An initial set of parameters characterizing the productive intervals, {k_(i),s_(i)} is determined by the conventional hydrodynamic study (HDS) of the well under the assumption that all formations have the same properties. For these parameters using the measured bottomhole pressure P₀(t) the total production rate of the well Q(t) and the relative production rates {y_(k) _(i) } of the individual perforation intervals are calculated. Then, using the found production rate Q (t) and the temperatures measured by the sensors mounted above the production layers using the procedure described above the relative production rates {y_(Q) _(i) } are found and the two obtained sets of numbers describing the inflow profile are compared, for example, the value of the discrepancy S is calculated:

$S = {\sum\limits_{i = 1}^{m}\; \left( {y_{Qi} - y_{ki}} \right)^{2}}$

If S is less than the specified value of the discrepancy ε:S<ε, then this set of parameters is adopted as the solution of the task. Otherwise, the values of the parameters {k_(i),s_(i)} are changed, and the calculations continue until the vectors {y_(k) _(i) } and {y_(Q) _(i) } coincide with a given accuracy. 

1. A method for determining a fluid inflow profile in a multilayer well, the method comprising: measuring a bottomhole temperature and a bottomhole pressure in a well by means of sensors mounted on a perforation string below all perforation intervals, wherein the measurements are made prior to perforating the well and after perforating the well until a temperature of a produced fluid returns to an initial reservoir temperature, measuring the temperature of the produced fluid by means of temperature sensors mounted on the perforation string above each perforation interval, estimating a total production rate of the well, calculating an excessive thermal energy of the produced fluid for each temperature sensor mounted on the perforation string above the perforation intervals, and determining production rates of the individual perforation intervals based on the calculated excessive thermal energies of the produced fluid and the known number of perforating charges in each perforation interval.
 2. The method of claim 1, wherein the total production rate of the well is determined by measuring a flow rate at the surface or in the well.
 3. The method of claim 1, wherein the total production of the well is determined by calculating a flow rate based on the change in the bottomhole pressure.
 4. The method of claim 1, wherein the total production of the well is determined by calculating a flow rate using the bottomhole pressure and numerically simulating the multilayer exploitation well. 